Question: $tu - 4tv - 9t + 8 = -4u + 6$ Solve for $t$.
Solution: Combine constant terms on the right. $tu - 4tv - 9t + {8} = -4u + {6}$ $tu - 4tv - 9t = -4u - {2}$ Notice that all the terms on the left-hand side of the equation have $t$ in them. $1{t}u - 4{t}v - 9{t} = -4u - 2$ Factor out the $t$ ${t} \cdot \left( u - 4v - 9 \right) = -4u - 2$ Isolate the $t$ $t \cdot \left( {u - 4v - 9} \right) = -4u - 2$ $t = \dfrac{ -4u - 2 }{ {u - 4v - 9} }$ We can simplify this by multiplying the top and bottom by $-1$. $t= \dfrac{4u + 2}{-u + 4v + 9}$